Chapter 7 · Kerala SSLC Class 10 Maths
Coordinates
Two ways to learn — a crisp formula reference, or a story that makes the maths feel obvious.
A story that builds each formula naturally.
How story mode works
Each scene is a real situation that naturally leads to a formula. Read the story, then tap "The Maths" to see the formula it maps to.
The GPS Map — Distance Formula
Aarav is a delivery driver using a GPS map on his phone. He needs to get from the warehouse at grid point A(1, 2) to a customer at B(4, 6). The roads run in a grid, but the app shows the straight-line distance.
I know how far east I have to go and how far north — can I just figure out the actual distance?
East distance: 4 − 1 = 3 units. North distance: 6 − 2 = 4 units. Those two legs form a right triangle.
East leg = 4 − 1 = 3
North leg = 6 − 2 = 4
Straight-line distance = √(3² + 4²)
= √(9 + 16)
= √25 = 5
The Pythagoras theorem on the grid gives exactly 5 units. That is all the distance formula is — Pythagoras applied to coordinates.
The Bridge Meeting Point — Midpoint and Section Formula
Meera lives at M(0, 0) and her friend Priya lives at P(8, 6). They want to meet exactly halfway — on a bridge over the river that cuts through the map.
Halfway between us — that's just the average of our positions, right?
Meeting x = (0 + 8)/2 = 4
Meeting y = (0 + 6)/2 = 3
Midpoint = (4, 3)
Later, a third friend Ravi wants to join them. He says he can only walk one-third of the total distance, so he wants the point that splits M→P in ratio 1:2 (he walks 1 part, Priya walks 2 parts from her side).
Section formula (1:2) from M(0,0) to P(8,6):
x = (1×8 + 2×0)/(1+2) = 8/3 ≈ 2.67
y = (1×6 + 2×0)/(1+2) = 6/3 = 2
Ravi's point ≈ (2.67, 2)
Calculating Land Area — Triangle Area Formula
A surveyor is measuring a triangular plot of land. The three corner pegs are at A(0, 0), B(3, 0), and C(0, 4) on the grid map. She needs the area for the land deed.
I know the coordinates — I don't need to measure sides. There's a direct formula for area from coordinates.
Area = ½|x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|
= ½|0(0−4) + 3(4−0) + 0(0−0)|
= ½|0 + 12 + 0|
= ½ × 12
= 6
The plot is 6 square units. Notice: if the area comes out 0, the three points are on the same straight line (collinear) — a useful check.
The big picture
Every formula in Chapter 7 is just arithmetic applied to (x, y) pairs. If you can average two numbers and do Pythagoras, you can do the whole chapter.
How far apart are two points?
d = √((x₂−x₁)² + (y₂−y₁)²)
What is the exact middle?
M = ((x₁+x₂)/2, (y₁+y₂)/2)
Where does a ratio divide the segment?
P = ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n))
What is the area of the triangle?
Area = ½|x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)|
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